Flight plan would help? Not too sure in this particular case.
As said, Mr. Fossett was flying to scout out dry lakebeds for a land-speed record attempt. By definition, that means just flying about until you find something, then circling around to check details etc. All this in a vast area of uninhabited land (desert?). His flight plan would not have contained anything useful in the "route" field. Not more than what we currently know already from friends who reported him missing.
Flight plans in the context of search and rescue are useful if you intend to fly a specific route, and do not deviate from it without informing ATC. But if you make sure that someone on the ground (in the UK context this is called a "responsible person") has the route information instead and knows your callsign, take-off time, EET and endurance, a flight plan does not offer much more information.
In the US, you can get "flight following" whether you filed a flight plan or not, and that's a far better investment, safety-wise. But from what I hear about the area, flight following might not be available there.